Problem: Solve for $x$ and $y$ using elimination. ${-2x-2y = -32}$ ${5x+y = 52}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${-2x-2y = -32}$ $10x+2y = 104$ Add the top and bottom equations together. $8x = 72$ $\dfrac{8x}{{8}} = \dfrac{72}{{8}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-2x-2y = -32}\thinspace$ to find $y$ ${-2}{(9)}{ - 2y = -32}$ $-18-2y = -32$ $-18{+18} - 2y = -32{+18}$ $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ You can also plug ${x = 9}$ into $\thinspace {5x+y = 52}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + y = 52}$ ${y = 7}$